4 Categorical Propositions
4.2 QUALITY, QUANTITY, AND
DISTRIBUTION
Quantity, Quality, and Distribution
Quantities: there are just two quantities:
1 Universal (All or None)
2 Particular (Some … at least one).
Qualities: there are just two qualities:
1 Affirmative
2 Negative
Quantity, Quality and Distribution
Proposition
All S are P
No S are P
Some S are P
Some S are not P
Letter Name
A
E
I
O
Quantity
Universal
Universal
Particular
Particular
Quality
Affirmative
Negative
Affirmative
Negative
Quantity and Quality are properties of Propositions.
A proposition is what a sentence asserts, or what we assert with a sentence.
‘I love the girl’ and ‘Puellam Amo’ are two different sentences that assert the same
proposition.
Quantity, Quality, and Distribution
Distribution is a property of terms, not propositions.
A term is distributed if the proposition asserts something about every
member of the class the term refers to, so…
In ‘All S are P’, something is asserted about every member of the class
referred to by the term S, and so S is distributed.
For instance, All Salads are Priced to sell … something is asserted
about every salad, but not about everything that is priced to sell (on
sale).
‘All S are P’ assigns or distributes a property to every member of S
(being priced to sell)
Quantity, Quality, and Distribution
All S are P can be symbolized like this:
S
P
Quantity, Quality, and Distribution
No S are P looks like this:
S
P
‘No S are P’, on our grocery interpretation, says something
about everything Priced to sell, and every Salad.
Therefore, both S and P are distributed.
Quantity, Quality, and Distribution
Some S are P:
S*
P
This says that at least one member of S is also a P (at least
one salad is priced to sell). This “I” proposition asserts
something about at least one member of S and at least
one member of P, so neither term is distributed.
Quantity, Quality and Distribution
Some S are not P:
S*
P
This propositions asserts that at least one Salad is not
Priced to sell (it says nothing about all salads, but it
does say something about all the sale items: none of
them is that particular salad—or subclass of salads).
Quantity, Quality and Distribution
Summary …
All SD are P
No SD are PD
Some S are P
Some S are not PD
Proposition
All S are P
No S are P
Some S are P
Some S are not P
Letter Name
A
E
I
O
Quantity
Universal
Universal
Particular
Particular
Quality
Affirmative
Negative
Affirmative
Negative
Distribution
Subject only
Sub & Pred
Neither
Predicate only